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The expression cos cos nos O O O O COS COS sin 5m 6 Л 6 5m sin 6 +sin-sin can be rewritten as which of the following?

The expression cos cos nos O O O O COS COS sin 5m 6 Л 6 5m sin 6 +sin-sin can be rewritten as which of the following?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question:** The expression \( \cos \frac{\pi}{2} \cos \frac{\pi}{3} + \sin \frac{\pi}{2} \sin \frac{\pi}{3} \) can be rewritten as which of the following? **Options:** - A) \( \cos \frac{\pi}{6} \) - B) \( \cos \frac{5\pi}{6} \) - C) \( \sin \frac{\pi}{6} \) - D) \( \sin \frac{5\pi}{6} \) **Explanation:** This problem requires applying trigonometric identities to simplify the expression. The expression given is in the form of the cosine of a sum identity, which is: \[ \cos A \cos B + \sin A \sin B = \cos(A - B) \] Using this identity, the expression can be simplified as: \[ \cos \left( \frac{\pi}{2} - \frac{\pi}{3} \right) = \cos \frac{\pi}{6} \] Therefore, the correct answer is option A) \( \cos \frac{\pi}{6} \).
Transcribed Image Text:**Question:** The expression \( \cos \frac{\pi}{2} \cos \frac{\pi}{3} + \sin \frac{\pi}{2} \sin \frac{\pi}{3} \) can be rewritten as which of the following? **Options:** - A) \( \cos \frac{\pi}{6} \) - B) \( \cos \frac{5\pi}{6} \) - C) \( \sin \frac{\pi}{6} \) - D) \( \sin \frac{5\pi}{6} \) **Explanation:** This problem requires applying trigonometric identities to simplify the expression. The expression given is in the form of the cosine of a sum identity, which is: \[ \cos A \cos B + \sin A \sin B = \cos(A - B) \] Using this identity, the expression can be simplified as: \[ \cos \left( \frac{\pi}{2} - \frac{\pi}{3} \right) = \cos \frac{\pi}{6} \] Therefore, the correct answer is option A) \( \cos \frac{\pi}{6} \).
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